Looking at the image, I can see this is an information sheet about tessellations. The key question posed in the text is:
"There are only three regular tessellations – can you find the other two?"
The sheet already shows one example: regular hexagons tessellate (fit together with no gaps).
Let me think through which regular polygons can tessellate:
A regular polygon can tessellate if its interior angles can fit together around a point to make exactly 360°.
For a regular polygon with n sides:
- Interior angle = (n-2) × 180° / n
Let me check common regular polygons:
1.
Equilateral triangle (n=3):
- Interior angle = (3-2) × 180° / 3 = 60°
- 360° ÷ 60° = 6 triangles can meet at a point
- ✓ Can tessellate
2.
Square (n=4):
- Interior angle = (4-2) × 180° / 4 = 90°
- 360° ÷ 90° = 4 squares can meet at a point
- ✓ Can tessellate
3.
Regular hexagon (n=6):
- Interior angle = (6-2) × 180° / 6 = 120°
- 360° ÷ 120° = 3 hexagons can meet at a point
- ✓ Can tessellate (this is shown in the image)
Let me check if any others work:
4.
Regular pentagon (n=5):
- Interior angle = (5-2) × 180° / 5 = 108°
- 360° ÷ 108° = 3.33... (not a whole number)
- ✗ Cannot tessellate
5.
Regular octagon (n=8):
- Interior angle = (8-2) × 180° / 8 = 135°
- 360° ÷ 135° = 2.67... (not a whole number)
- ✗ Cannot tessellate
So the three regular tessellations are made from:
- Equilateral triangles
- Squares
- Regular hexagons
Since the image already shows hexagons, the other two are triangles and squares.
Final Answer:
The other two regular tessellations are made from equilateral triangles and squares.
Parent Tip: Review the logic above to help your child master the concept of tessellation worksheet pdf.
